Central Intelligence Agency
The CIA (also known as "The Company") is a US intelligence agency, formerly known as the Office of Strategic Services (OSS). Disbanded after WWII, the OSS became the CIA during the Cold War. The CIA has been controversial, having at times been accused of incompetence, immoral actions, or both. Given their involvement in projects like MKULTRA, it's not all that surprising. When they appear in fiction alongside the FBI, the CIA is often portrayed as bad, and the FBI good, and with good reasons.
Federal Bureau of Investigation
Originally known as the Bureau of Investigations (BOI), the FBI is the primary investigative arm of the US Department of Justice (DOJ). It serves as both the principal federal criminal investigative body, and a domestic intelligence agency. The FBI is automatically called in if a crime crosses state lines, or for crimes that don't but yet fall under federal jurisdiction, such as foreign spies on US soil. The Mafia is very fond of interstate crimes, and is hence the FBI's public enemy #1.
British Secret Intelligence Service
The SIS, almost always referred to in media by the term "MI6" ('Military Intelligence, Branch 6'), is the external intelligence agency for the United Kingdom, roughly equivalent to the United States' CIA. The SIS also has a domestic counterpart, called 'MI5'. The agency's reputation in media is inextricably linked to the James Bond mythos, and the its appearances in media tend to either play to, or directly contradict such notions. Carmen briefly worked for MI6 before signing on for the CIA.
Komitet Gosudarstvennoy Bezopasnosti
The KGB, known as the 'Committee for State Security' in English, is the main security agent of the Soviet Union from 1954 until its fall in 1991. It is a direct predecessor of the MGB, and as well as the NKVD, NKGB, and Cheka before it. The KGB is the Soviet equivalent to the British MI6, and the Americans' CIA, thus making it their sworn enemy. Vinzenz briefly worked for the KGB via Operation Osoaviakhim, when it was still known as the MGB.
National Crime Syndicate
The National Crime Syndicate was the name given by the press to the multi-ethnic, loosely connected American confederation of criminal organizations. It is a confederation that mostly consisted of the Italian-American Mafia and Jewish mob, but also included some other ethnic crime groups. In short, the Syndicate is the empire of the criminal underworld. The FBI long denied a syndicated involvement between the Italian, Russian-Jewish, and French mobs until the 1957 Apalachin criminal convention.